Use a dedicated type instead of a reference for the diagnostic context

This paves the way for tracking more state (e.g. error tainting) in the diagnostic context handle

src/driver.rs

@@ -180,12 +180,12 @@ pub fn main() {
 
     rustc_driver::init_rustc_env_logger(&early_dcx);
 
-    let using_internal_features = rustc_driver::install_ice_hook(BUG_REPORT_URL, |handler| {
+    let using_internal_features = rustc_driver::install_ice_hook(BUG_REPORT_URL, |dcx| {
         // FIXME: this macro calls unwrap internally but is called in a panicking context!  It's not
         // as simple as moving the call from the hook to main, because `install_ice_hook` doesn't
         // accept a generic closure.
         let version_info = rustc_tools_util::get_version_info!();
-        handler.note(format!("Clippy version: {version_info}"));
+        dcx.handle().note(format!("Clippy version: {version_info}"));
     });
 
     exit(rustc_driver::catch_with_exit_code(move || {